Question

1. describe the transformations in g(x)=2|x - 1|+5 as it relates to the graph of the parent function.

Explanation:

Step1: Identify the parent function

The parent function of $g(x)=2|x - 1|+5$ is $f(x)=|x|$.

Step2: Analyze horizontal shift

For the form $y = |x - h|$, here $h = 1$. A positive $h$ value means a right - shift. So, there is a horizontal shift of 1 unit to the right.

Step3: Analyze vertical stretch

The coefficient of the absolute - value function is $a = 2$. When $|a|>1$, it causes a vertical stretch. So, the graph of the parent function is vertically stretched by a factor of 2.

Step4: Analyze vertical shift

The constant term $k = 5$. A positive $k$ value means a vertical shift upwards. So, there is a vertical shift of 5 units up.

Answer:

The graph of $g(x)=2|x - 1|+5$ is the graph of the parent function $y = |x|$ shifted 1 unit to the right, vertically stretched by a factor of 2, and shifted 5 units up.